THE ROLE OF ANALYSIS IN THE RATE-PROCESSES

Numerical solutions are now possible for a much wider range of conditions than analytical (continuous) ones and are gradually supplanting them in our literature. The results obtained from numerical solutions as well as from analytical solutions in the form of series, integrals, or tabulated functions are more precise, regular, and coherent than experimental data but are always subject to some uncertainty owing to idealizations made in developing the model itself. Both types of solutions fail to provide a functional structure for correlation, thus giving rise to the tabulations, graphical correlations, and purely empirical equations to be found in our handbooks. On the other hand, asymptotic solutions which do provide such a functional structure can generally be derived not only for extreme conditions but for intermediate regimes as well. Comprehensive correlating equations of great accuracy can often be constructed from two or more asymptotic solutions with almost no empiricism. Examples are given of the determination of asymptotes by reduction of more general solutions, by direct derivation, and by dimensional and speculative analysis, and also of their combination. Examples from the existing literature are given of invalid or inapplicable asymptotes and combinations thereof as well.